SOLUTION: The sum of the digits of a two digit number is 10 .If 18 is subtracted from it the digits in the resulting number will be equal. Find the required number.

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Question 981507: The sum of the digits of a two digit number is 10 .If 18 is subtracted from it the digits in the resulting number will be equal. Find the required number.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The result of the two digits being equal means this is a multiple of 11;
so use an extra variable, n, for either of these resulting digits.
Your multiple of 11 is some 11*n, and n must be a digit.

Your unknown number, 10t%2Bu;
t for your tens, u for your ones.

Your transcribed information will then be
system%28t%2Bu=10%2C10t%2Bu-8=11n%29
.
system%28t%2Bu=10%2C10t%2Bu-11n-8=0%29

u=10-t
substitute.
10t%2B%2810-t%29-11n-8=0
9t-11n%2B2=0
9t=11n-2
t=%2811n-2%29%2F9

Pick to test values of whole number n from 1 to 9 to find which will give
a whole number result for t.

n__________________resulting t
1___________________1
2___________________x
3___________________x
4___________________x
5___________________x
6___________________x
7___________________x
8___________________x
9___________________x

Only n=1 gives a whole value for highlight%28t=1%29.
With that t, what is u?
u=10-t
u=10-1
highlight%28u=9%29

Your unknown number is then 10%2A1%2B9=10%2B9=highlight%28highlight%2819%29%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the digits of a two digit number is 10 .If 18 is subtracted from it the digits in the resulting number will be equal. Find the required number. 
Number you're looking for: highlight_green%2873%29